Fantasy Freestyle

The PFM, My Bid Limits, and You

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Throughout the positional tier series and continuing throughout my bid limit articles, some of our readers have been asking questions and raising objections along the following lines:

I don’t understand why your bid limit on Paul Goldschmidt is $36 in NL-only when the PFM only has him at $29.20. I know everyone is really excited about Goldschmidt this year, but I’m relying on the PFM for my auction and I don’t understand why there is a $7 difference between your suggested bid and the PFM’s. What gives?

For more than a few readers, I suspect there is a misunderstanding of what PECOTA/the PFM is designed to do versus what my bid limits are designed to do.

(Before you dive into this piece, I strongly urge you to read Rob McQuown’s 2014 introduction to PECOTA if you have general questions about PECOTA and the PFM. My article is not intended to reinvent the wheel when it comes to explaining PECOTA and the PFM, but rather to showcase the difference between PECOTA and my bid limits.)

As noted in Baseball Prospectus’s glossary, PECOTA has three elements incorporated into its projection model:

1) Major-league equivalencies, to allow us to use minor-league stats to project how a player will perform in the majors;
2) Baseline forecasts, which use weighted averages and regression to the mean to produce an estimate of a player's true talent level;
3) A career-path adjustment, which incorporates information about how comparable players' stats changed over time.

The most important component to consider for fantasy valuation is item #2. The forecasts offer projections that incorporate regression to the mean and weighted averages for every player. For a projection system this is appropriate; in fact, it would be a poor projection system if it predicted something silly like “Chris Davis is going to hit 53 home runs” or “Miguel Cabrera is going to have a .348 batting average.” Yet this is exactly what happened in 2013. Something PECOTA will not do is project the inevitable outliers and – to reiterate this vital point – it most definitely should not.

Nearly every fantasy analyst is not factoring regression to the mean and weighted averages into his bid limits, and my bid prices are no exception. Rather, we are all attempting to offer recommendations based upon the market price for the best hitters and pitchers available at your auction.

According to PECOTA, Braun and Trout are projected to have the best fantasy seasons in the National League and American League. But Braun is “only” projected to earn $35 while Trout is “only” projected to earn $37. A $37 projection is certainly a reasonable one for Trout given that it’s only six dollars less than what the PFM said he earned last year. But LABR doesn’t know from PECOTA. LABR’s $45 bet is saying it believes that a 22-year-old stud hitter will continue to get better as he moves up the age curve.

This is only part of what LABR’s price reflects. LABR recognizes that Trout could put up a $37 season, as the PFM suggests. To take this even a step further, LABR recognizes that Trout could have a down year and even if he stayed completely healthy earn only $25-30. Trout’s buyer understands the fact that there is a good chance that Trout won’t have a $45 season. The bet here isn’t on Trout having a $45 season but rather on the idea that Trout is the most likely hitter in the American League to return $35 or more worth of statistics.

While this principle isn’t quite as extreme with the other most expensive hitters, it still applies. Nearly every hitter in this bracket is being paid for his ceiling, and PECOTA is correct that there is a good chance that nearly all of these hitters will fail to get there.

Table 2: Top 10 Salaries, AL/NL Only Hitters, 2009-2012

Year/League

$

Avg Sal

+/-

CBS

LABR

Tout

2013 AL

$26

34

-8

33

34

34

2012 AL

$24

35

-11

35

35

34

2011 AL

$24

36

-12

41

35

32

2010 AL

$25

35

-10

38

33

32

2009 AL

$24

36

-12

41

33

34

2013 NL

$22

35

-13

35

35

35

2012 NL

$28

37

-10

37

37

37

2011 NL

$33

38

-6

42

36

36

2010 NL

$28

39

-10

42

37

36

2009 NL

$31

40

-9

44

39

36

Table 2 shows the 10 most expensive hitters using the average salary from three expert leagues—CBS, LABR, and Tout Wars—from 2009 through 2013. The expert market pays these hitters with the expectations that will perform as well or slightly better than they did the year before, but the harsh reality is that these hitters disappoint their fantasy owners year in and year out, losing about $10 per hitter on average for the last five years.

PECOTA might miss on individual hitters on a case-by-case basis, but it has a far better handle on the big picture than the fantasy experts do. If this is the case, why should you bother with my bid limits? Doesn’t this exercise simply prove that my bid limits are worthless and that the PFM is more accurate?

Remember that part of the operating premise of this article is that as a prognostication tool PECOTA works quite well and is not what is at issue here. PECOTA looks at the future and correctly predicts regression for the top hitters on a macro level. Next, the PFM takes PECOTA’s forecast and applies it to fantasy values, also doing a good job based on the stats that PECOTA generates. I quibble with how much value the PFM gives to stolen bases and saves (even with the SGP option turned on) and believe that the mono-league formulas give too much credence to the concept of the replacement level fantasy player, but the dollar values are generally sound. A $2 difference between my 2013 Paul Goldschmidt valuation and the PFM’s 2013 Goldschmidt isn’t a gaping chasm.

My bid limits are different than the PFM valuations not because PECOTA is right and I’m wrong, but because we are serving two different masters. Where PECOTA is trying to construct a reality based upon a regression-based data model, I have devised a system that is attempting to navigate the dynamics of a fantasy baseball auction. My bids do something that the PFM cannot: adjust for the real world dynamics of a fantasy baseball auction.

Since 2011, Miguel Cabrera has earned $36, $40, and $42 according to my valuations (the PFM says $31, $39, and $41). I look at these earnings, see a 31-year-old four-category deity, and put my bid limit at $42. Am I betting on a repeat of 2013? No. In fact, if I ran my own mechanical projections I would probably show Cabrera putting up a $35-37 season. So why am I willing to possibly take a $5-7 loss on Cabrera?

I look back at retrospective fantasy baseball earnings and know between seven to fifteen hitters will earn $30 or more in mono formats. My bids are guessing which hitters are most likely to earn $30 or more. I know that I’m going to get some of my guesses wrong, but because anywhere between 7-15 hitters are going to earn $30 or more, my bids are structured so that about 10-12 hitters have a bid limit of $30 or higher.

This is what the auction marketplace does as well. The expert market doesn’t look at PECOTA or any of the non-Baseball Prospectus projection systems and shy away from spending over $30 on all but Trout and Cabrera. It places bets on the hitters it believes are most likely to crack the $30 barrier, and bets based on what happened last year, not what might happen this year. The market is aware that it is going to miss on some hitters (and miss big on a few hitters) but doesn’t care because the market isn’t trying to factor in regression but is trying to buy statistics.

Despite the big losses among the most expensive hitters year in and year out, they still earn the most money nearly every season. You need value and profit to win but you have to procure enough statistics. This is why the market overpays for the top hitters. Because the market is overpaying the best hitters, the hitters at the end of the auction are relative bargains. Some one-dollar hitters are going to flame out and lose money, but all it took in 2013 was Brian Dozier to skew the profit margins for the cheap hitters way up.

If you religiously use the PFM’s values in an auction, it is likely you will struggle to purchase players early, get a lot of players in the middle of your auction, and end the day leaving some money unspent. The PFM is “paying” the full freight for what certain players might do if they play full time, while the auction market is conservative. For example, perhaps the PFM is correct and Josh Rutledge will earn $16.72 in 2014. It’s certainly possible that he can do this if he wins the second base job over D.J. LeMahieu, but his purchase prices thus far have been three dollars (CBS) and seven dollars (LABR). If want Rutledge badly enough and believe my five dollar bid limit is ridiculously conservative, you should push it higher but $17 is way too much. No one is going to pay that much for Rutledge. $10-12 should do it.

I have been doing this for so long that I don’t need to look at a projection system before I put my bids together. I simply do what I did above with Miguel Cabrera above for most of the available player pool. I review recent earnings, guess what I believe the player will earn this year based on a combination of fantasy earnings, sabermetric data, and any changes in his real-life circumstances and make an educated guess. Then in cases like Rutledge’s I move the bid down to reflect what I think the player should actually cost in an auction-style marketplace.

Hopefully, I have convinced you not to go into your auctions solely using the PFM valuations and to use my bid limits as a baseline instead. However, if you still believe that my bid limits contain too much of the human element and adamantly believe that the PFM is superior, I recommend making the following adjustments.

1) Turn the SGP feature ON.
Please, please, please, if you do nothing else make sure that the SGP Level in PECOTA is turned “ON” before you start using it as an auction baseline. Below is a screenshot of what this should look like before you run the PFM.

If you don’t do this, one-dimensional stolen base threats and closers will be valued extremely highly and there’s a good chance that you will walk out of your auction with Billy Hamilton, Eric Young, Craig Kimbrel, and Kenley Jansen at a combined salary of $100 or more. You’ll win saves and steals going away but will fail to acquire the balance that you need to win.

2) Don’t Pay The Bench Guys
While it’s possible that the PFM is right and John Mayberry will earn $8.97 or Chris Heisey will earn $8.75, there is no rational reason to bid more than two or three dollars for a bench outfielder, even in an only format, when most of these types are going to cost no more than $1-3.

This applies even more for middle relievers. Some middle reliever is surely going to do what Neal Cotts did last year and earn $15 or more in middle relief, but there’s no reason to pay more than $1-2 for a middle reliever when there are so many relievers sitting in the free agent pool, and trying to predict who the best middle relievers will be in fantasy is an exercise in pure guesswork.

I would recommend taking the money from the bottom and moving it to the top, but if you agree with PECOTA and are afraid of regression, move that money to the middle. Just make sure you’re not wasting your bid money on bench players you can get for $2-3 at the end quite easily.

3) Make Sure You Spend All Of Your Money
You don’t have to pay $30 or more for a player at your auction; in fact, my bid limits are quite conservative compared to CBS and LABR-AL, and I have been spending anywhere from $24-27 on my most expensive player in most of my auctions so far this year. However, my bid model reflects the reality of how owners spend their money in auctions so that I ensure that regardless of how I distribute my auction cash, I do make sure that I spend it.

You don’t want to overspend on one of top hitters, but it’s even worse to panic and pay $40 for Puig because he was the last top-tier player on the board (in the PFM’s model) and you didn’t want to get caught with a lot of money at the end of the auction. My bid limits ensure that you will spend your money in your auction. Even if you don’t agree with my bid limits for specific players, take the structure of the bid limits (the pricing hierarchy) and use them as a jumping off point. Points #2 and #3 are closely tied together. Even in an only league, there are going to be anywhere from 12-24 one dollar hitters and 10-15 one dollar pitchers in the end game. Make sure that your bid limits reflect how teams and owners spend in your league’s auction dynamic.

You are not competing against PECOTA or the PFM but against the other owners in your league. The bid limits I have constructed have the built-in assumption that most Rotisserie-style leagues are similar to CBS, LABR, and Tout Wars in the way that they allocate their auction dollars. Feel free to disagree with my rankings on a player-by-player basis, but the logic behind how I distribute the bids across the player pool is sensible and borne out by my real life Roto auction experience.

Thank you very much for explaining the differences in rationales between your bid system and the PFM. I also appreciate your sharing of PFM settings. The PFM glossary and tooltips are concise, but insufficient without more background information.

Regarding the SGM button, considering the scarcity of SB and saves shouldn't you pay a little more for the players? I have seen many teams over the years who just punt those categories in order to 'save money'. Wouldn't overpaying for Kimbrel or Hamilton get you at least a few more points in the middle of the category that overpaying on Trout or Miguel Cabrera wouldn't? They aren't going to hit 30 extra homers but Hamilton (should) get 50 SB even if that's all he contributes.

It's not a matter of paying a little more, it's a matter of acquiring too many. You want to get enough to do well in the category, but without SGP the PFM will try to help you own the category at the expense of others.

The "market price" is already adjusting for this. Sinking 1/5th of your pitching budget into a non-elite closer in a 5x5 is quite a lot of money when you think about it. Spending more than that is where you run the risk of spending "too much" on a category.

These are great rules of thumb, but the question I have is basically, why isn't this something the PFM is trying to do?

Or at least, why isn't there a setting to have the PFM do this? These don't seem like intractable concepts, mathematically - if they are accurate, then they should be measurable and the PFM should be able to compensate for it. So really, what is happening here is that the PFM is an imperfect tool because it makes projections and then treats those projections the way it would treat end-of-season data (and even there it does it poorly, because it doesn't account for time on the DL vs. playing).

It would be really cool if the PFM could be upgraded to try to incorporate this type of information. I see 3 main steps to this:

1) Deal better with PT uncertainty.
a) Projecting dollar value based on PT estimates needs to incorporate whether or not that estimate is affected by injury chances, job competition, etc. Hanley was worth a lot last season while he was playing. If he's projected to miss 100 PAs this season, those 100 PAs should be added back in at replacement-level rates when calculating his value.
b) Someone who might or might not play due to competition is a different story. They are a case of basically %chance to play vs. expected performance when they do play. So again, their total should be $10 if they have a 50% chance to be worth $20 and 50% chance to be replaced (as opposed to taking their stats, dividing them by 2, and then asking how much that player is worth)

2) Improved replacement level calculations for fantasy.
a) Replacement level isn't just the expected performance of the best guy just outside the top N. That's the easiest thing to calculate, but it's really pretty wrong. About 30% of the value earned by teams in my league last year came from guys who were not on teams to start the year.
b) The better calculation is basically, what is the expected production of all PAs/IPs that will actually be had by players in lineups. This is not easy to get at, but a quick improvement is essentially accounting for the fact that if we look at a points league with 200 hitters active, and hitters #196-205 are projected at 415-385 points, the expected earnings of that bunch is not 400 points/slot. It's a lot higher, because the 5 guys who do the best will get the slots.

3) "Spend all your money"
a) This is obviously more nebulous, but the idea here is basically this: when the draft is done, I should be able to judge how I did by adding up the projections of my players, and comparing that to the projections of players on the other teams.
b) The main thing that could be incorporated here is while inflation might cause the value of the last good shortstop to skyrocket, and paying that value would be correct at that moment, the better play would be to keep yourself from being the guy who ends up paying that. Overpay $5 for Hanley, so you don't end up overpaying $10 for Segura or Desmond. If this isn't already handled by valuations, it needs to be (and if it is, then you should never pay more than the PFM estimate unless you think the PFM projection itself is faulty).

Couldn't agree more. The ability to place auction values on players in a systematic, quantitative way is a big part of what I thought I was paying for at BP. PFM is way overdue for upgrades before next season, and the comment above (and to a certain extent the article itself) illustrate some of the reasons why.

I actually completely disagree. PFM takes the most likely statlines and compares them against the 288th best player in the pool to come up with values. Skewing it to a higher valued "replacement player" makes little sense and no other fantasy site does it that way. Padding stats for injury-prone players who *might* get a full-season of at bats makes less sense. Giving theoretical values to players who aren't likely to get called up (like Gregory Polanco) would just dilute the amount of money available.

FWIW, I think the SGP level and the centric inflation will already accomplish most of what you're requesting in this post.

To adjust for auction realities, you would need a setting that applies "x" bid limit to "y" level of valuation, which i haven't seen in any projection system for fantasy. You would ultimately have to project the injuries we can't see coming in February to get Mike Trout and Miguel Cabrera to the $40+ they actually earn in the retrospective PFM and you would have to have an awareness of which hitters/pitchers would tank and be worth $1 or negative bids. The paradox is that while you could offer projections like this, the projections themselves would be silly even if in fact they made the PFM's valuation model. more "correct".

I think this adjustment falls outside the projection system. The "correct" auction price for premium players really does exceed their nominal projected value. Similarly, the auction price for scrubs should be less than their projected nominal value.

I wrote this:
http://www.baseballprospectus.com/article.php?type=2&articleid=23061#156750
before I saw your comment. I think there is a real economic basis for the differences between auction prices and nominal projected value.

Love this discussion, thanks for humoring me - this is exactly the sorts of topics I was excited to see discussed with the expanded fantasy coverage. Wall of text incoming...

Even though we can't predict who will be injured, who will have unexpectedly poor performances, and who will have unexpectedly good ones, we can still estimate the odds of those things occurring. Even if those estimates are useless/unreliable on an individual level, we could at least apply the aggregate chance to everyone.

What we would see, I suspect, is basically what you're describing in the article, but with the ability to more easily adjust to different formats/leagues sizes/etc. Guys who are close to but just above replacement level will have the bottom part of their performance curve cut off, and thus bleed value to the guys below replacement level (who would have even more of their curve cut off). Guys like Trout and Cabrera would lose no value (except to the injury chances), and you could calculate the built-in inflation by looking at how much value you were projecting for the below-replacement guys.

For example, there are about 9350 runs, 8800 RBI, 2300 HR, 1700 SB and 17800 hits to be had from above-replacement players in a 12 team yahoo standard league (which has 10 hitters and 8 pitchers per team), according to the PFM. If I go down to guys worth at least -$3, the totals increase to about 10000 R, 2450 HR, 9400 RBI, 1800 SB, and 19000 Hits, representing 10 more hitters (at an average of about 65/14/60/9/129 in 496 ABs). If I go up to >$1, I cut out 10 hitters, who perform at an average of about 68/16/64/13/129 in 496 ABs. Now a full analysis would know the real projected distribution of each stat for each player, but just as a wild guess, let's say that the difference in the average stats equals 1 standard deviation. With that assumption, we are saying that about 3 of the hitters in the sub-replacement 10 will out perform the 3 worst of the above-replacement 10. The level of performance will therefore be the average of the top 7 players in the first group + the top 3 in the second group (to a first approximation). So this ups the overall totals for this group by 12.5 R, 8.5 HR, 17.4 RBI, 13.4 SB, and 2.2 hits. That ranges from 1-6% for the counting stats, and a lot less for the hits (which is a sub for BA), but more importantly it told us that the ~7 positive dollars assigned to last 10 hitters should really be more like $4.90 (the 7/10 guys who won't be out-produced). Since you can't actually spend the extra $2 on guys beyond the roster size, it naturally gets spread to the rest of the guys in proportion to how good they are (with Trout and Cabrera getting more of it than anyone else).

I'll note here that I tossed in some numbers to make the math easy that aren't really good numbers to use - the +$1 / -$3 barriers were totally arbitrary, the assumption that they represented 1 standard deviation of performance is almost certainly not true, and treats the stats as composites, instead of looking at each stat individually is obviously a bad way to do it. But hopefully this outlines the general approach I'm talking about. Would be cool to see it applied to the PECOTA percentile performances, but I don't have any good way to do that without a whole lot of manual data entry.

But Mike, PFM already has the Aggressive/Conservative slider, couldn't the same logic be pursued even further to include an appropriate amount of over-bidding on elite talents?

Here is the problem I find myself with -- I can easily take free projections very similar to PECOTA's for every player in the league, rank hitters/starters/closers in the right order, and then just apply the 1st/2nd/3rd/etc highest bids from tout wars or LABR for the same category of player. The weakness of that approach is the difficulty I would have in accurately assessing the relative value of SB vs HR, of saves versus ERA contribution, etc. Another weakness is knowing whether the internal dymanics of those auctions caused errors to be made in the distribution of valuations (stars/scrubs vs balanced). How do I value roster flexibility, probable replacements for injury-prone guys, etc. Those hard questions are where BP fantasy can really add value for a veteran player. But, if PFM does a bad job of valuing catagories relative to eachother, and doesn't even attempt to do the other things, then I guess I shouldn't be using it.

The Aggressive/Conservative slider has the same problem that the PFM does. Even with the SGP turned on, it adds more money to SB/saves guys at the top than it does to the power hitters/ace starting pitchers.

It's a preemptive response to the late inflationary pressure in an auction draft. The glut of late round $1-$2 bargains (relative to nominal value) produces de-facto retroactive inflation among the rest of the player pool. If you won't pay more than $25 early in the draft for a player that PFM values at $25, you are failing to take into account the retroactive inflationary pressure that happens at the end of every auction draft since the dawn of time.

Inflation occurs during an auction, EVERY auction, as a result of variations in evaluation. In order to purchase a player, you must (in general), bid MORE than 11 other owners have a player valued at. Therefore, you are creating inflation for every other valuation, even if YOU think the purchase is at value. This effect is true for every early purchase, before position scarcity and reduced $$$ reduce inflation.

Which means, that inflation ALWAYS occurs, so the $2 bargains are not bargains because 11 other owners made mistakes, but because a different evaluation tool was used early. So even if EVERYONE thinks a $6 player is worth $6, there is never enough money left to allocate to all of those players.

The question is, should we use the PFM to adjust for that, or is that the owners responsibility?

The above point about adding Replacement level value to Injury risks is a good one, the argument could be made for any Minor Leaguer, or part time player. But the problem is, this is fine on a micro level (fixing hanley) but if we fix EVERY part time/injury player, what the hell is going to happen to the over $$$...

Anyway, PFM needs some modifiers for replacement levels, and theoretical auctions, because this year it is just Out-To-Lunch, much more than any other year I've seen.

The problem with relying on an in-auction tool is that in an auction with 20% inflation if the first 40 players cost $80 over the tool's price, then you are tricking yourself into thinking there will be deflation in your auction. But that's not really how it works, because teams still have the same amount of money to spend and will keep "overspending". Every team in the league will keep spending at the 20% inflation rate, but you'll wait and wait until it's too late and leave a lot of money behind. I've seen it happen and it isn't pretty.

MG: "My bids do something that the PFM cannot: adjust for the real world dynamics of a fantasy baseball auction."

When you buy a Jeff Keppinger type player, there is a very real risk that he will play his way off your roster. I am tempted to call that an "opportunity cost", but I could be mis-using the term. In other words, low-end players should be valued for even less than their meager projections, because you will likely need to spend more to fix your roster. A failure to meet nominal performance requires replacing them.

The top players, may not meet their nominal dollar values, but they will still provide decent performance. That certainty is worth a premium beyond their projected value. Their roster spot is in good hands.

I think this explains the "retroactive inflationary pressure" coined in an earlier comment.

It would seem possible to build that kind of auction price adjustment into the PFM.

Not sure I agree. In fact, you NEED some low-value players to play their way off your roster quickly so you can have FA flexibility early in the season. The ones who kill you are those late and mid round picks who chug along at 70-80 percent of predicted production so you don't have a clear rationale to drop them.

During the course of the year 2430 wins will be obtained by some pitcher. Someone has to get the win correct? Due to the conservative nature of the software the SP have what seams like low win totals. Is the PFM a zero sum game and so have all the "Win" stats allocated to some pitcher? if so who if the PFM being bullish on? RP's or SP's out of the top 50? Thanks.